Hi, I'm afraid I can't help you with the Moscow question - I'm travelling in February so it's something I want to find out myself! The Man in Seat 61 (http://www.seat61.com/) has a page on the Trans-Siberian express with lots of information and tips on how to buy tickets, including links to websites where you can buy them online.

You can buy tickets online - I bought mine through a company called Sokol Tours. They arrange to meet you at the station and give you the tickets for each leg of the journey (or arrange place for you to pick them up). By booking online, I ended up paying about $US 1000 for $US 250 worth of tickets. Therefore, you can save a significant amount by booking yourself at the stations. Therefore, if you are willing to try and deal with the ticket agents at the train stations, I would suggest buying them there. I don't think you'd have a problem with getting seats / bunks during November.

Note that you need to buy point-to-point tickets for specific trains, so if you want to stop and see some sights along the way (which I would recommend, both because there are some really nice things to see, but also because you'll probably go crazy on the train for seven days otherwise), you'll need to buy tickets between your specific destinations.